6239.0 - Barriers and Incentives to Labour Force Participation, Australia, July 2014 to June 2015 Quality Declaration 
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 03/05/2016   
   Page tools: Print Print Page Print all pages in this productPrint All

TECHNICAL NOTE DATA QUALITY

INTRODUCTION

1 Since the estimates published in this publication are based on information obtained from occupants of a sample of households, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all households had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of households (or occupants) was included.

2 There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all households had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs.

3 Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate.

RSE% = (SE/estimate) x 100

4 RSEs for Barriers and Incentives to Labour Force Participation estimates have been calculated using the Jackknife method of variance estimation. This process involves the calculation of 30 'replicate' estimates based on 30 different sub-samples of the original sample. The variability of estimates obtained from these sub-samples is used to estimate the sample variability surrounding the main estimate.

5 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *13.5) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g.**2.1) to indicate that they are considered too unreliable for general use.

CALCULATION OF STANDARD ERROR AND RELATIVE STANDARD ERROR

6 RSEs are routinely presented as the measure of sampling error in this publication and related products. SEs can be calculated using the estimates (counts or means) and the corresponding RSEs.

7 An example of the calculation of the SE from an RSE follows. The table shows that the estimated number of males aged 18–24 years who did not prefer to work more hours is 205,800, and the RSE for this estimate was 18.0%. The SE is:

SE of estimate
= (RSE / 100) x estimate
= 0.18 x 205,800
= 37,000 (rounded to the nearest 100)

8 Therefore, there are about two chances in three that the value that would have been produced if all households had been included in the survey would fall within the range 168,800 to 242,800 and about 19 chances in 20 that the value would fall within the range 131,800 to 279,800. This example is illustrated in the following diagram.

Picture 1: Calculation of standard error or relative standard error

Proportions and percentages

9 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSEs of proportions not provided in the spreadsheets is given below. This formula is only valid when x is a subset of y.

Equation 1: Proportions and percentages formulae

10 Considering the table, of the 968,600 males who usually worked 0–34 hours each week, 649,400 or 67.0% did not prefer to work more hours. The RSE of 649,400 is 5.5% and the RSE for 968,600 is 4.7%. Applying the above formula, the RSE for the proportion of males who did not prefer to work more hours is:

Equation 2: Proportions and percentages example

11 Therefore, the SE for the proportion of males who usually worked 0–34 hours per week who did not prefer more hours was 1.9 percentage points (= (67.0/100) x 2.9). Therefore, there are about two chances in three that the proportion of males who usually worked 0–34 hours per week who did not prefer more hours is between 65.1% and 68.9%, and 19 chances in 20 that the proportion was within the range 63.2% to 70.8%.

Sums or Differences between estimates

12 Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers, means or percentages) where these are not provided in the spreadsheets. Such estimates are also subject to sampling error.

13 The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x–y) may be calculated by the following formula:

Equation 3: Sums or differences between estimates formulae

14 The sampling error of the sum of two estimates is calculated in a similar way. An approximate SE of the sum of two estimates (x+y) may be calculated by the following formula:

Equation 4: Sums or differences between estimates formulae

15 An example follows. From Paragraph 7 the estimated number of males aged 18–24 years who did not prefer to work more hours was 205,800 and the SE was 37,000. From the table, the estimate of males aged 25–34 years who did not prefer to work more hours was 105,200, and the SE was 15,990. The estimate of males aged 18–34 years who preferred not to work more hours is:

Equation 4: Sums or differences between estimates example

16 The SE of the estimate of males aged 18–34 years who did not prefer to work more hours is:

Equation 5: Sums or differences between estsimates example

Equation 5: Sums or differences between estimates example

17 Therefore, there are about two chances in three that the value that would have been produced if all households had been included in the survey would fall within the range 270,700 to 351,300 and about 19 chances in 20 that the value would fall within the range 230,400 to 391,600.

18 While these formulae will only be exact for sums of, or differences between, separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all sums or differences likely to be of interest in this publication.

SELECTED ESTIMATES AND RSES

PERSONS AGED 18 YEARS AND OVER, USUALLY WORKED 0–34 HOURS PER WEEK OR NOT EMPLOYED, Whether wanted a job or more hours—By age


PERSONS WHO USUALLY WORKED 0–34 HOURS PER WEEK
PERSONS NOT IN THE LABOUR FORCE
Preferred to work more hours
Did not prefer to work more hours (a)
Total
Unemployed
Wanted a job (b)
Did not want a job (a)
Total
ESTIMATES ('000)

Males
Age group (years)
18–24
96.2
205.8
304.8
88.0
113.5
105.9
212.5
25–34
72.9
105.2
180.3
87.3
53.8
*46.0
120.0
35–44
45.3
64.4
107.3
58.4
56.7
50.5
108.6
45–54
42.5
79.4
123.9
38.0
42.5
126.5
168.6
55 and over
51.7
209.4
260.9
44.7
221.1
1,450.3
1,679.3
Total
309.4
649.4
968.6
312.6
473.0
1,778.7
2,293.0
Females
Age group (years)
18–24
174.6
242.5
412.6
101.8
101.8
156.5
287.6
25–34
112.6
314.1
434.9
72.9
143.1
288.0
444.3
35–44
134.6
464.5
596.6
71.4
150.0
256.6
410.8
45–54
135.0
358.4
490.7
71.3
81.6
264.0
353.3
55 and over
82.5
457.4
534.2
35.4
213.1
1,929.2
2,152.2
Total
628.4
1,824.4
2,458.5
356.2
699.2
2,896.4
3,642.0
Persons
Age group (years)
18–24
261.6
438.7
700.2
203.4
215.6
250.0
489.2
25–34
185.3
419.1
607.3
153.5
201.8
335.6
569.3
35–44
177.3
525.2
698.6
134.1
202.7
306.9
523.7
45–54
179.8
436.2
613.2
107.6
129.5
387.5
518.8
55 and over
137.5
664.6
800.9
79.2
430.4
3,383.9
3,834.7
Total
946.7
2,486.0
3,429.8
673.1
1,165.4
4,671.4
5,941.6
RSES OF ESTIMATES (%)

Males
Age group (years)
18–24
16.3
18.0
11.1
19.5
18.0
16.4
11.1
25–34
19.6
15.2
12.8
14.1
20.2
27.3
16.8
35–44
23.4
11.9
13.0
14.3
16.9
16.1
9.1
45–54
20.4
15.3
11.1
20.9
20.4
8.8
7.5
55 and over
16.3
8.9
7.1
12.2
9.4
1.9
1.3
Total
10.5
5.5
4.7
8.0
6.0
2.0
1.8
Females
Age group (years)
18–24
14.8
12.0
7.5
17.6
19.1
17.9
7.9
25–34
16.2
6.8
5.3
15.3
9.2
6.0
4.1
35–44
10.9
3.8
3.5
11.9
8.9
6.2
3.3
45–54
10.9
4.0
4.1
12.4
15.3
5.8
3.4
55 and over
15.0
5.4
4.6
15.6
6.0
1.0
1.0
Total
5.8
2.1
1.7
7.1
5.0
1.2
1.1
Persons
Age group (years)
18–24
11.0
11.2
6.4
3.2
11.6
11.9
2.2
25–34
13.3
5.6
5.0
3.6
6.8
5.3
1.8
35–44
10.7
3.6
3.8
4.0
7.1
5.8
1.5
45–54
9.5
3.6
3.5
3.7
10.4
3.9
1.8
55 and over
11.5
5.1
3.7
5.0
6.3
0.9
0.4
Total
5.1
2.3
1.8
1.6
3.5
1.0
0.5

* estimate has a relative standard error of 25% to 50% and should be used with caution
** estimate has a relative standard error greater than 50% and is considered too unreliable for general use
np not available for publication
(a) Includes persons who reported 'Did not know'.
(b) Includes persons who reported 'Maybe/it depends'.

SIGNIFICANCE TESTING

19 A statistical test for any comparisons between estimates can be performed to determine whether it is likely that there is a significant difference between two corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 13. This standard error is then used to calculate the following test statistic:

Equation 6: Significance testing formulae

20 If the value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a difference between the populations with respect to that characteristic.

21 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.